Question

向量题目

设e1,e2是夹角为45°的两个单位向量，且a=e1+2e2,b=2e1+e2,求|a+b|

Answer 1

|a+b|=|e1+2e2+2e1+e2|=|3e1+3e2||a+b|^2=9(e1+e2)^2=9(e1^2+e2^2+2e1e2)e1^2=e2^2=1 e1e2=|e1||e2|cos<e1,e2>=1*1*cos45=√2/2 2e1e2=√2|a+b|^2=9(2+√2)|a+b|=3√(2+√2)

Answer 2

a+b=(e1+2e2)+(2e1+e2)=3(e1+e2)
|a+b|=3|e1+e2|
=3[|e1|²+|e2|²-2|e1|·|e2|cos(180º-45º)]
=3[1+1+2·1·1·(√2)/2]
=6+3√2